Five Lectures on Dissipative Master Equations
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The family of propagators E(t2,t1) is completely positive for all t2 ≥ t1 if and only if L_t has the Kossakowski-Lindblad form for any time t.
“Similarly to the case of time-independent equations, it can be shown that the family E(t 2 , t 1 ) is completely positive for all (t 2 t 1 ) if and only if L t has the Kossakowski-Lindblad form for any time t [13].”
From Markovian master equations: a critical study (2010) · cites this paper as [13]
Cites
Risken, H. (1984) · Springer series in synergetics · doi:10.1007/978-3-642-61544-3 · Cited by 9,128 · see citing works
On the generators of quantum dynamical semigroups
Lindblad, G. (1976) · Communications in Mathematical Physics · doi:10.1007/bf01608499 · Cited by 7,548 · see citing works
Scully, M. O., & Zubairy, M. S. (1997) · doi:10.1017/cbo9780511813993 · Cited by 6,589 · see citing works
Manipulating quantum entanglement with atoms and photons in a cavity
Raimond, J. M., Brune, M., & Haroche, S. (2001) · Reviews of Modern Physics · doi:10.1103/revmodphys.73.565 · Cited by 2,669 · see citing works
Walls, D. F., & Milburn, G. J. (1994) · Springer eBooks · doi:10.1007/978-3-642-79504-6 · Cited by 2,197 · see citing works
Schleich, W. P. (2001) · Wiley eBooks · doi:10.1002/3527602976 · Cited by 1,928 · see citing works
Gardiner, C. W., & Zoller, P. (2000) · Springer series in synergetics · doi:10.1007/978-3-662-04103-1 · Cited by 1,377 · see citing works
Meystre, P., & Sargent, M. (1990) · Springer eBooks · doi:10.1007/978-3-662-07007-9 · Cited by 905 · see citing works
Statistical Structure of Quantum Theory
Holevo, A. S. (2001) · Lecture notes in physics. M, Monographs · doi:10.1007/3-540-44998-1 · Cited by 747 · see citing works
Observation of sub-Poissonian photon statistics in a micromaser
Rempe, G., Schmidt‐Kaler, F., & WALTHER, H. (1990) · Physical Review Letters · doi:10.1103/physrevlett.64.2783 · Cited by 572 · see citing works
Preparing pure photon number states of the radiation field
Varcoe, B. T. H., Brattke, S., Weidinger, M., & WALTHER, H. (2000) · Nature · doi:10.1038/35001526 · Cited by 381 · see citing works
Wigner function as the expectation value of a parity operator
Royer, A. (1977) · Physical Review A · doi:10.1103/physreva.15.449 · Cited by 376 · see citing works
Quantum optical master equations: The use of damping bases
Briegel, H., & Englert, B. (1993) · Physical Review A · doi:10.1103/physreva.47.3311 · Cited by 239 · see citing works
Self-citationParity operator and quantization of δ-functions
Großmann, A. (1976) · Communications in Mathematical Physics · doi:10.1007/bf01617867 · Cited by 197 · see citing works
Sub-Poissonian atomic statistics in a micromaser
Rempe, G., & WALTHER, H. (1990) · Physical Review A · doi:10.1103/physreva.42.1650 · Cited by 136 · see citing works
Conditions for compatibility of quantum-state assignments
Caves, C. M., Fuchs, C. A., & Schack, R. (2002) · Physical Review A · doi:10.1103/physreva.66.062111 · Cited by 105 · see citing works
General theory and applications to unstable particles
Alicki, R. (2008) · Springer eBooks · doi:10.1007/3-540-18276-4_5 · Cited by 96 · see citing works
One-atom maser: Statistics of detector clicks
Briegel, H., Englert, B., Sterpi, N., & WALTHER, H. (1994) · Physical Review A · doi:10.1103/physreva.49.2962 · Cited by 87 · see citing works
Self-citationOn the operator bases underlying Wigner's, Kirkwood's and Glauber's phase space functions
Englert, B. (1989) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/22/6/015 · Cited by 64 · see citing works
Self-citationParity states in the one-atom maser
Englert, B., Sterpi, N., & WALTHER, H. (1993) · Optics Communications · doi:10.1016/0030-4018(93)90254-3 · Cited by 51 · see citing works
Self-citationOn the Structure of Covariant Dynamical Semigroups
Holevo, A. S. (1995) · Journal of Functional Analysis · doi:10.1006/jfan.1995.1089 · Cited by 44 · see citing works
Quantum-optical master equations: An interaction picture
Englert, B., Naraschewski, M., & Schenzle, A. (1994) · Physical Review A · doi:10.1103/physreva.50.2667 · Cited by 43 · see citing works
Self-citationHow much state assignments can differ
Brun, T. A., Finkelstein, J., & Mermin, N. D. (2002) · Physical Review A · doi:10.1103/physreva.65.032315 · Cited by 41 · see citing works
On conservativity of covariant dynamical semigroups
Holevo, A. S. (1993) · Reports on Mathematical Physics · doi:10.1016/0034-4877(93)90044-f · Cited by 39 · see citing works
Spectral decomposition of the Lindblad operator
Barnett, S. M., & Stenholm, S. (2000) · Journal of Modern Optics · doi:10.1080/09500340008232202 · Cited by 33 · see citing works
Vacchini, B. (2002) · Journal of Mathematical Physics · doi:10.1063/1.1505126 · Cited by 29 · see citing works
Macroscopic dynamics of a maser with non-Poissonian injection statistics
Briegel, H., & Englert, B. (1995) · Physical Review A · doi:10.1103/physreva.52.2361 · Cited by 28 · see citing works
Self-citationWhose KnowledgePreprint
Mermin, N. D. (2001) · arXiv (Cornell University) · Cited by 20 · see citing works
Fock states in a cyclically pumped one-atom maser
Brattke, S., Englert, B., Varcoe, B. T. H., & WALTHER, H. (2000) · Journal of Modern Optics · doi:10.1080/09500340008232201 · Cited by 18 · see citing works
Self-citationLaser experiments with single atoms and the test of basic quantum phenomena
WALTHER, H. (2001) · Optics and Spectroscopy · doi:10.1134/1.1405208 · Cited by 12 · see citing works
The Interpretation of Quantum Mechanics: Many Worlds or Many Words?
Tegmark, M. (1998) · Fortschritte der Physik · doi:10.1002/(sici)1521-3978(199811)46:6/8
Self-citation
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Rivas, Á., K Plato, A. D., Huelga, S. F., & B Plenio, M. (2010) · New Journal of Physics · doi:10.1088/1367-2630/12/11/113032 · Cited by 258 · see citing works
Markovian master equations: a critical studyPreprint
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Fazio, R., Keeling, J., Mazza, L., & Schirò, M. (2025) · SciPost Physics Lecture Notes · doi:10.21468/scipostphyslectnotes.99 · Cited by 57 · see citing works
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Mora, C. M., & Rebolledo, R. (2008) · Americanae (AECID Library) · Cited by 38 · see citing works
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Mora, C. M., & Rebolledo, R. (2008) · The Annals of Applied Probability · doi:10.1214/105051607000000311 · Cited by 36 · see citing works
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Davis-Tilley, C., & Armour, A. D. (2016) · Physical Review A · doi:10.1103/physreva.94.063819 · Cited by 25 · see citing works
Entanglement of distant atoms by projective measurement: the role of detection efficiency
Zippilli, S., Olivares-Rentería, G. A., Morigi, G., Schuck, C., Rohde, F., & Eschner, J. (2008) · New Journal of Physics · doi:10.1088/1367-2630/10/10/103003 · Cited by 20 · see citing works
Self-citationSteady Fock states via atomic reservoir
Prado, F. O., Rosado, W., Neto, G. D. D. M., & Moussa, M. H. Y. (2014) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/107/13001 · Cited by 19 · see citing works
Lindblad dynamics of a quantum spherical spin
Wald, S., & Henkel, M. (2016) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/49/12/125001 · Cited by 19 · see citing works
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Hush, M., Lesanovsky, I., & Garrahan, J. P. (2015) · Physical Review A · doi:10.1103/physreva.91.032113 · Cited by 19 · see citing works
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Dhahri, A. (2008) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/41/27/275305 · Cited by 18 · see citing works
Observing different quantum trajectories in cavity QED
Santos, M. F., & Carvalho, A. R. R. (2011) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/94/64003 · Cited by 18 · see citing works
Concha, J. I., & Poor, H. V. (2004) · IEEE Transactions on Information Theory · doi:10.1109/tit.2004.826637 · Cited by 18 · see citing works
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Avron, J. E., Kenneth, O., Retzker, A., & Shalyt, M. (2015) · New Journal of Physics · doi:10.1088/1367-2630/17/4/043009 · Cited by 9 · see citing works
Rosado, W., Neto, G. D. D. M., Prado, F. O., & Moussa, M. H. Y. (2015) · Journal of Modern Optics · doi:10.1080/09500340.2015.1051150 · Cited by 9 · see citing works
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Harvey, T. J., Rodrigues, D. A., & Armour, A. D. (2010) · Physical Review B · doi:10.1103/physrevb.81.104514 · Cited by 6 · see citing works
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Turner, R. M., Speck, T., & Garrahan, J. P. (2016) · Cited by 6 · see citing works
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- Authors
- Englert, B.-G., & Morigi, G.
- Affiliations
- Max Planck Institute of Quantum Optics (DE)
- Universität Ulm (DE)
- Venue
- Lecture Notes in Physics
- Publisher
- Springer Berlin Heidelberg
- Published
- 2002
- Pages
- 55-106
- ISSN
- 0075-8450 (ISSN-L)
- OpenAlex
- W1623949636
- Cited by
- 46
- References
- 31
- Citations by year
- 2026: 1 · 2025: 1 · 2023: 1 · 2022: 2 · 2021: 3 · 2020: 3 · 2019: 4 · 2018: 2 · 2017: 1 · 2016: 3 · 2015: 4 · 2014: 2 · 2013: 1 · 2012: 1
- FWCI
- 4.51
- Type
- book chapter
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Lecture notes in physics (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum optics and atomic interactions
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
- Keywords
- damped harmonic oscillator, open quantum systems, quantum optics, phase-space functions, masers
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